Kije Sipi. Kije Sipi Ltd. Weather Radar Derived Rainfall Areal Reduction Factors

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1 Ltd Weather Radar Derived Rainfall Areal Reduction Factors J. P. Jolly 1, D. I. Jobin 1, S. Lodewyk 2 1. Ltd, Ottawa ON, Canada 2. City of Edmonton, Edmonton AB Canada ABSTRACT Rainfall Areal Reduction Factors (ARF) are often used in hydrology to volumetrically adjust pointbased rainfall statistics for application over large watershed surfaces. Existing ARF factors are derived using point-based rainfall data from meteorological stations and carry the inherent limitations associated with typically low density network data. This paper reports findings from analyzing seven years of gauge adjusted weather radar data in deriving ARFs and characterizing the spatial distribution of rainfall events occurring over and near the City of Edmonton, Canada. ARFs were derived from a pool of over 250 storm events and expressed as a function of the type of storm, duration, geographical extent and maximum rainfall intensity. Furthermore, each storm event was identified and characterized according to a set of hydrological criterion from a 1km 2 gridded, 15- minute radar database. Comparisons were completed with existing ARF relations, and findings indicated the potential of creating higher spatial resolution ARF functions using weather radar data. Leclerc and Schaake (1972) reanalyzed the Bureau s data and expressed the ARFs as an exponential function of rain area and duration. In 1960, Woolhiser and Schwalen determined an ARF function for convective rainstorms occurring over Arizona, USA. The independent variables in this case are rain area and maximum point rainfall. This equation is applicable to rain area up to 40 km 2. It is believed that no other major similar analyses were undertaken until weather radar signals started to be used for hydrologic applications. Omolayo (1993) showed that the 1 and 24-hr fixed area determined ARF values developed by the USWB can be used in Australia for areas ranging between 200 and 300 km 2. His analysis is based on the assumption that ARF values are a function of rain area and rainfall duration and not return period i.e. Rmax. Allen and DeGaetano (2005) evaluated the USWB analysis using more data than available at the time of the original study (between 5 and 16 years) by studying ARFs determined by the fixed-area method for rain areas less than 1000 km 2 for two US regions approximately 18,000 km 2 in size - one in New Jersey and the other in North Carolina. Both had rain gauge density better than one gauge per 1000 km 2. The ARF relations developed for the two regions are in general agreement with TP- 29 results for rain areas less than 1000 km 2 ; however, the study revealed several important facts: INTRODUCTION Until the mid twentieth century, there were no means of determining a storm spatial average rainfall except in the few regions where there were high densities of rain gauges. In the US Weather Bureau (now NOAA) developed some areal reduction factors (ARFs) that could be used to determine spatial average rainfalls from maximum point values based on rainfalls measured at twenty dense rain gauge networks located in various regions of the United States (Eagleson, 1970). The developed relations gave ARF as a function of rain area and duration. The Bureau s curves (usually referred to as the TP-29 curves) applied to rainfalls with approximately 1:2- year return period (Allen and DeGaetano, 2005). The results were given in graphical form and were included in the WMO 1982 Probable Maximum Precipitation Guide. 1) ARF varies with return period,i.e., Rmax; 2) April-September ARF values are lower than the October-March ones; and, 3) there are only modest differences in ARF values between the two regions, which differ significantly in geography. Both regions are in the mid latitudes of the contiguous United States at locations where most of the storms that produce the largest rainfalls are fronts and tropical systems. In the following sections the development of ARF relations will be described for the region surrounding Edmonton, Alberta, Canada. It has a different hydrometeorologic regime than the others. The mid latitude of the study area is 52 degree north - much higher than the other study areas. The study region s summer heavy rainfalls are caused by either convective storms without the Page 1 / 10

2 Ltd concurrent occurrences of frontal rainfalls or convective storms embedded in frontal rainfalls. Most of the studies undertaken to date have been carried out using the geographic fixed-area method that is used to estimate rainfalls of particular return periods from point rainfalls. The storm-centered method of calculation ARFs has been mainly used in probable maximum precipitation studies (Omolayo, 1993); however, the latter method was used in this study because of the small areal extents of the region s summer storms with high maximum point rainfalls (Rmax> 20 mm) and the steep spatial rainfall gradients of these storms. Table 1 Study Area Period of Analysis Area (km2) , , , , No Data , , , ,618 Average 22,900 GENERAL APPROACH The purpose of this paper is to report upon an analysis of the spatial distributions of rainstorms occurring over and near the (take out the bolding) City of Edmonton and their associated areal reduction factors in the non-winter period. The rainfall data was obtained from two sources: one, the regional rain gauges and, two, from rainfall values obtained from weather radar signals that were ground truthed with the regional rain gauge data. This provided seven years of rainfall totals occurring during the May-September period on a 1 km 2 grid out on a 120 km radius. The yearly analysis period was taken to be the interval of May through September when the majority of the rainfalls occurs in this region. The highest storm rainfall depth also occur in this period. mainly in convective rain cells. The study area is mainly confined to the broad valley of the North Saskatchewan River. Regions of high elevations were masked as well as areas where erroneous rainfall values were produced by the radar signals. Table 1 lists the size of the study area for each available year of radar data. The tabulation indicates a generally stable study area size with an average of about 23,000 km 2 for the seven years of data. The 2001 radar data could not be retrieved from the archives due to electronic problems with the hard drives. The number of rain gauges used varied in each yearly calibration. The numbers per year are given in Table 2. Table 2 Number of Rain Gauges Used for Calibrations Period of Analysis Number of Rain Gauges No Data The hydrometeorological criteria used to identify rainstorms are: 1. minimum rainfall intensity per radar grid cell greater than 0.2 mm/hr; 2. inter-event spacing of equal or less than four radar grid cells (1km 2 ); and, 3. inter-event time of equal or less than six hours. BASIC STATISTICS Several key storm rainfall statistics were obtained including the number of storms with maximum total rainfalls greater than 5 mm as presented in Figure 1. Page 2 / 10

3 Ltd Figure 1: Distribution of Storms by Maximum Rainfall (Rmax >5 mm) Number of Storms Storm Count by Maximum Peak Rainfall Accumulation Count 105 Peak Total Rainfall (mm) The bar chart shows the number of storms, in increments of 10 mm, for the entire range of maximum total rainfalls that are greater than 5 mm. A total of 1,791 storms that occurred in the seven years were identified. The largest storm rainfall in the database has approximately 180 mm of total rainfall; however, the majority of all storms (~66%) have less than 20 mm of maximum total rainfall. Six hundred and eighty storms were identified that had maximum grid rainfalls higher than 20 mm, although only 518 were used in the analyses. The others were excluded because the locations of maximum point rainfalls were too close to study area boundaries that areal reduction factors could not be calculated. There were no summer frontal storms found without convective rain cells with maximum rainfalls greater than 20 mm convective cell, or cluster of cells, usually less than 200 km 2 in extent. Accumulation of the Storms Convective cells can occur as single entities - such as the example shown in Figure 2. The figure indicates that total rainfall varies from a maximum total rainfall of 30 mm to less than 5 mm over approximately a 100-km2 area. There are no other rain cells and no rainfall totals larger than 5 mm within a 625-km2 area surrounding the convective cell. This type of storm has been given the identification label SCC (Single Convective Cell). On many occasions throughout the summer months, a number of individual convective cells can occur close to each other. One is depicted in Figure 3, where five convective rainfall cells are shown. The largest radar grid cell rainfall total is 54 mm while the four other convective cells have maximum point rainfalls larger than 30 mm. The total area shown in the figure is 1,200 km 2, and the average distance between locations of the individual grid cell maximum rainfall location is 6 km. Figure 2: Type of Storm Single Convective Cell (SCC) STORMS TYPE The spatial distribution of rainfall occurring over an area is generally dependent on the storm type. For example, frontal and convective storms have different temporal and spatial precipitation distributions that produce quite different surface water accumulations. Consequently, storms were classified by type. The nomenclature used in identifying each type of storm was developed for this study and consequently might not strictly adhere to standard meteorological convention. The rainfalls that occur in the study area are mainly of two types: one is frontal rain system that passes over the region; the other is a smaller 10 km This type of rainstorm pattern has been labeled in this study as CLCC, which is short for CLuster of Convective Cells. Page 3 / 10

4 Ltd Figure 3: Type of Storm CLuster of Convective Cell (CLCC) 1 km Frontal storms have been represented in the technical literature as large areas of relatively uniform rainfall totals occurring over long durations. The phrase relatively uniform rainfall totals was deemed as inapplicable for this study area. A review of the regional storms indicates that most large-areal extent; long-duration summer storms have non-uniform rainfall totals. In most cases, the pictorial views of the spatial distributions of total rainfalls have wavy surface appearances such as in the example shown in Figure 4. This particular graph shows the storm rainfall totals over a 6,600-km 2 surface area. The rainfall varies from 25 to 105 mm and increases from the southeast to northwest sector with two peaks of significant rainfall (>80 mm) that are approximately 53 km apart. Since the individual cell maximum rainfall totals occur over great distances, the rain area surrounding each maximum rainfall location is individually pertinent. Thus this type of rainfall occurrence has been labeled SCF for Single Cell in Frontal storm. Figure 4:Type of Storm Single Cell in Frontal Storm (SCF) There are also occasions when several local storm cell maximum rainfall totals occur close together within a frontal system and the cell rainfalls can be classified differently than a single cell in a frontal storm, since the local maximum rainfalls are close enough together that more than one local maximum rainfall could occur over a 100- or 200- km 2 area. Hence many individual convective cells could deposit rainfall on to a small watershed. Figure 5 presents such a case in which the rainfall storm event occurs over a 2,400-km 2 area. In this example, there are six individual rainfall maximums with an average maximum to maximum distance of seven km. The total rainfall varies from 5 to 76 mm over the area; however, half the area has rainfall totals greater than 30 mm. This type of storm has been labeled CLCF for CLuster of Cells in Frontal storm. Figure 5: Type of Storm Cluster of Cells in Frontal Storm (CLCF) Each storm event analyzed in this study was grouped in one of these four storm categories, and analyses were conducted on the pertinent data of each group. 10 STORM SPATIAL CHARACTERISTICS Two hydrometeorological terms are used to characterize the spatial reduction of storm rainfalls. The first is Spatial Decay Ratio (SDR) that is defined as the storm average rainfall for a specific rain area divided by the storms maximum (point) rainfall independent of rainfall duration. The other term is Areal Reduction Factor (SRF), which is defined as the storm average rainfall for a specified rain area that occurs over a particular duration divided by the maximum point rainfall that occurs over the same duration (WMO, 1982). In order words, SDRs pertain to a storm s total Page 4 / 10

5 Ltd rainfall; whereas, ARFs pertain to a storm s rainfall occurring over a particular duration, or a specific time interval within a storm duration. From examination of the radar imagery of convective storm rainfalls, it was determined that many convective storms consist of two or more separate convective cells each with a local maximum storm rainfall. It was recognized that more than one of these discrete convective cells could occur either concurrently or nearly concurrently (within basin lag) over a small watershed. Thus the spatial characteristics of both discrete (single) convective cells and clusters of concurrent, or quasi-concurrent, close-together convective cells were determined. generalized forms of the two- and three-parameter equations are: Table 3 Basic SDR Data Statistics Storm Basic Statistics Rmax=>20 mm Single Cell Cluster of Cells Convective Frontal Subtotal Convective Frontal Subtotal Total Number of Storm Number of SDR Curve Number of SRD Point Minimum SDR Maximum Rain Area (km^2) Minimum Duration(hr) The spatial average rainfalls of a storm were determined using the storm-centered method by totaling the rainfalls that occurred on the grids enclosed within circular areas emanating from the grid of maximum rainfall and then averaging. The values of the spatial decay ratios are plotted against the corresponding concentric areas outward from the location of a storm maximum rainfall for both frontal and convective storms as well as convective cells within frontal storms. Table 3 gives basic statistics on the entire SDR dataset broken down by storm type. Research by others has indicated that ARF values vary directly with storm duration and inversely with storm rain area and, in some cases, with maximum total rainfall (Woolhiser & Schwalen, 1960, and Allen&DeGaetano, 2005, and USWB. 1963). These three independent variables were tested during this study and found to vary with SDR values. Consequently equations were developed using either two or three of these variables for each of the four storm types. These equations were developed using 518 SDR curves (storm cells) that are defined by over 5,000 points. Twenty-nine equation types were investigated, and the equation parameters as well as goodness-of-fit statistics were determined by regression analyses or coefficient optimizations. Two best equations were selected: one is a twoparameter equation, and the other is a threeparameter one. The former has rain area and rain duration as the independent variables; the latter has rain area, rain duration and maximum grid (point) rainfall as the independent variables. The Maximum Duration (hr) Maximum Cell Rainfall (mm) Average Maximum Cell Rainfall(mm Number of SDR Points Area (km^2) Two Parameter Function (Equation 1) b a * D ARF = ( c + A) Where area A is in km 2, duration D is in hr and, a, b, c and d are optimized coefficients. Three Parameter Function (Equation 2) ARF = a + b* ln( A) + c*ln( D) + d *ln( RMax) Where Rmax is the total rainfall at the radar cell with the maximum rainfall, in mm. The values of the optimized coefficients for both equations and the four types of storms are listed in Table 4. The table also presents goodness-of-fit statistics including the Coefficient of Determination and the Standard Error of Estimate (hereafter referred as to standard error) for each equation. Considering the hydrometeorological nature of the datasets, the results are considered to be quite good. d Page 5 / 10

6 Ltd Table 4: ARF Optimized Parameters and Goodness-of-Fit Statistics Areal Reduction Factor Function Coefficients Coefficient Storm Type Symbol A B C D Coefficient of Determination Standard Error Two-Parameter Equation (Function # 12) Single Convective Cell SCC Cluster of Convective Cells CLCC Single Cell in Frontal System SCF Cluster of Cells in Frontal System CLCF There-Parameter Equation (Function # 18) Single Convective Cell SCC Cluster of convective Cells CLCC Single Cell in Frontal System SCF Cluster of Cells in Frontal System CLCF Moreover, the goodness-of-fit statistics are better for the convective cells (either simple or in clusters) not in frontal rainfalls and very good for the single convective cells. The two-parameter equations have slightly better coefficients of determination than the three-parameter equation for the convective cells not embedded in frontal storms; however, the opposite is true when the frontal storms are considered. Nevertheless, in all four cases the standard errors for all equations are generally the same - at approximately 10%. Rain areas up to 1000 km 2 were used in the equation developments. The coefficient optimization method weighs solutions toward the centroid; hence the large number of SDR points associated with small rain areas significantly biases the function fits. Since there are more data points in the lower half of this range than the other, it is assumed the resulting equations are valid for rain areas less than 500 km 2. Figures 6 and 7 show the ARF curve for all four storm types for the 6 hr duration. Figure 6: Areal Reduction Factors 3-Parameters AREAL REDUCTION FACTOR AREAL REDUCTION FACTORS - 3 PARAMETER EQUATIONS Dr=6hr; Rmax=42 mm RAIN AREA (km^2) Figure 7: Areal Reduction Factors 2-Parameters AREAL REDUCTION FACTORS -TWO PARAMETER EQUATION Dr=6hr SCC CLCC SCF CLCF As a result, the function coefficients were determined using SDR points with only up to 500 km 2 in Area and 24 hours or less in Duration. The goodnesses of fit are better for the convective storms not occurring in frontal systems than those embedded. In comparing the results in terms of whether the two- or three-parameter equations are better, it appears that the two-parameter equations give better results for convective cells that are not part of a frontal system and the three-parameter equations give better results when convective rainfalls are embedded in fronts. Moreover, in all cases the equations are better for single storms than clusters. AREAL REDUCTION FACTOR RAIN AREA ( km^ 20 Figure 6 gives the values associated with the twoparameter equations; figure 7 shows the values associated the three-parameter equations. In both cases the ARF values for rain cells in frontal Page 6 / 10 SCC CLCC SCF CLCF

7 Ltd rainfall are higher than those of the independent single cells and clusters. Moreover, rainstorms with six-hour durations do not have large differences between single and cluster ARF values. The two-parameter ARF Equation derived for Clusters of Cells in Frontal systems (CLCF) was selected out of the eight choices tabulated in Table 4 as the design ARF equation for hydrologic analyses in small watershed because the ARFs are higher for frontal storms and the highest rainfall that occurred in the seven-year record was of this rainstorm type. Hence it is the most conservative curve (less areal reductions in rainfall). Although the three-parameter equation could also have been selected, it is believed that the two-parameter exhibited more consistent results at the upper end of the surface area range. ARF = 1.0 e (1.1* D 0.25 Where D is in hr and the A is in mi 2. ( 1.1* D 0.01* A) Figure 8: USWB Areal Reduction Factors (WMO, 1982) ) + e 0.25 Equation 3 below presents the final form of the proposed ARF function ARF * D = ( A) Where A is in km 2 and D is in hr. COMPARISONS OF DEVELOPED ARFs WITH THOSE OF OTHER STUDIES The first study on this subject was undertaken by the United States Weather Bureau (NOAA, 1963). The results were published by that organization (see Figure 8). Also the graph of the study ARF versus Area up to 1,000 km 2 for various storm durations was also published in the WMO Manual for Determination of Probable Maximum Precipitation (1982). This study on rainfall spatial distribution did not differentiate the data by the various storm types. Moreover, it is believed that these curves were developed from data of storms that had an approximate return period of two years (Allen and DeGaetano, 2005) Furthermore, the ARF curves were established using only rain gauge data from a low-density network compared to the 1km-by-1km radar grid used in this study. Leclerc & Schaake (1972), using either values taken from the USWB curves in the abovementioned WMO graph or the data points from which the curves were developed, gives an equation that relates ARF to rain area and duration. The equation (Equation 4) is expressed as: Woolhiser&Schwalen (1960) conducted a similar study. Their equation is currently believed to be the only one to express the ARF in terms of area and maximum point rainfall. It is applicable in convective storm areas of 40 km 2 or less in Arizona, USA. Their equation can be expressed as: 0.6 ARF = 1.0 (0.14* A )/ RMax Where A is in mi 2 and Rmax is in inch. A cursory graphical comparison of the current study findings with both the Leclerc & Schaake s (USWB/WMO) and the Woolhiser & Schwalen s ARF relations was undertaken. The results are presented as Figure 9. The TP-29 curve depicts the results obtained using Leclerc & Schaake equation, and the (W&S) gives the results by using Woolhiser & Schwalen results while the two others (2-P and 3- P) present the current study findings. The two curves from this study were produced using the Single Convective Cell (SCC) type of storms, which is the type of storm for which the Woolhiser Page 7 / 10

8 Ltd & Schwalen equation was developed. Figure 9 gives values up to 50 km 2 in area because the Woolhiser & Schwalen study data only covered storms up to 40 km 2. Nevertheless, the TP-29 study results show very little spatial rainfall reduction with area and less than the other two datasets while the Woolhiser & Schwalen curve is close to the current study curves. Figure 9: Comparison of ARF Single Convective Cell, RT=2yr; Dr=6hr; Rmax=28 mm COMPARISON OF ARF - SINGLE CONVECTIVE CELL - RT=2yr; Dr=6hr; Rmax=28mm independent variables and can be compared to the result obtained from the LeClerc & Schaake s equation (TP-29). As previously indicated, for small rain areas the latter equation gives much higher ARF values. Moreover, the equations represent rain total characteristics of different regions and were developed from quite different data forms. The three-parameter Edmonton equation provides values that cannot be directly compared with those of the other two studies since the latter are only two-parameter equations area and duration in the case of LeClerc & Shaake; and area and maximum total rainfall (Rmax) in the case of Woolhiser & Schwalen s study. AREAL REDUCTION FACTOR RAIN AREA (km^2) Applying hypothetical rain areas, durations and RMaxs gives a more rigorous comparison of these four equations. The results are given in Table 5. The selected rain areas are 40, 200 and 1,000 km 2 and the two durations are 2 and 6 hours. The one-in-five year Edmonton point rainfall total for each of these two durations was applied. Table 5: Comparison of Study CLCF ARFs with Others COMPARISON OF AREAL REDUCTION FACTORS CLCF STORMS AREA (km^2) DURATION (hr) :5 yr Rmax(mm) TP-29 Study - 2P Study - 3P W&S The Woolhiser & Schwalen s study gives ARF values for convective rainfall storms for rain areas up to 40 km 2 only, which is comparable in size to some of the rain clusters analyzed in this study. The Woolhiser & Schwalen s ARF values for the 2 and 6-hours, 1:5-year rainfalls are lower than those obtained in this study. This is most likely because of the two study areas have different hydrometeorological regimes. Moreover, the storm duration is not taken into account in the Wolhiser & Schwalen s equation development. Areal Reduction Factor (ARF) Figure 10: Edmonton Areal Reduction Function Edmonton Areal Reduction Function (by Duration) 15 Min 30 Min 45 Min 1 Hr 1.5 Hr 2 Hr 4 Hr 6 Hr 8 Hr 10 Hr 12 Hr 14 Hr 16 Hr 18 Hr 20 Hr 22 Hr 24 HR Two-Parameter Three-Parameter TP Wolhiser&Schwalen The 40-km 2 -area was selected because it is the upper limit of applicability of the Woolhiser & Schwalen s equation. The 200 km 2 - rain area was selected because it is approximately the upper limit of typical storm sewer systems. It is impossible for direct comparisons to be made of the calculated ARF values determined in this study and those of the other two studies; however, this is difficult. The two-parameter Edmonton equation has rain area and duration as the Area (km2) In Figure 10 the ARF curves produced by applying the two-parameter cluster of convective cells in frontal storms are given. They are applicable for areas up to 500 km 2 and for durations from 15 min to 24 hr for the Edmonton region. Page 8 / 10

9 Ltd CONCLUSIONS 1. Four distinct total rainfall spatial patterns were identified from a large storm database. These rainfalls occur from two separate sources: convective and frontal storms. The convective rainstorms can occur as isolated single cells or as a few cells in close proximity to one other in a storm. Hence four distinct types of storms were named: Single Convective Cell CLuster of Convective Cells Single Cell in Frontal system CLuster of Cells in Frontal system 2. Spatial Decay Ratios (SDR) were calculated for radar grid cells within each storm that had a maximum total rainfall greater than 20 mm. Five hundred and eighteen SDR curves described by over 5,000 points were computed. Furthermore, SDRs were grouped according to the four types of storms in order to develop sets of Areal Reduction Factors Functions. 3. ARF equations were determined following an extensive trial-and-error search through candidate relations. This resulted in a selection of two equations with strong goodness-of-fit values. 4. A comparison with the results of two other research studies was made. The current study shows considerably larger amounts (degrees) of spatial decay of rainfall than given the WMO (1982) report. However, rigorous comparisons were difficult since the type of storms, the surface areas and locations as well as type of source data (point rain gauge versus radar) were considerably different. Nevertheless, the cited study by Woolhiser & Schwalen (1960) does corroborate a rapid decay of rainfall amounts for convective storms. 5. The equations developed in this study are based on seven years of rainfall data. As more weather radar is archived, further equation development can be undertaken with larger data sets that will enable the equations to be refined and be more statistically accurate. SUGGESTED RESEARCH No method of obtaining ARF values is error free. There are also unknown errors in rain gauge readings and stream measurements which hydrologists have learned to live with. Radar-rain gauge calibration errors have been categories by Ahnert etal (1983) as (1) rain gauge sensor errors, (2) radar sensor errors and (3) sampling errors introduced by the difference between a point measurement and the overhead radar grid value. Although not much can be done to reduce rain gauge sensor errors, it is recommended that efforts continue to minimize the errors associated with the other two sources thereby improve the precisions of spatial rainfall statistics. In this study and the others citied, rainstorm duration is one of the factors that the ARF values depend. In all storms and especially for convective storms the maximum rainfall time series is not uniform and some cases highly non-uniform. Research is required in order to obtain more meaningful values than the difference between start and end of storm rainfall. This and other related studies have storm spatial average maximum rainfall as the end result. For designs of hydraulic structures and schemes in small basins quite often the maximum rainfall intensity over a specified interval is the more important parameter. Preliminary results from this study indicate that the location of maximum grid intensity is quite often not at the same location as the maximum storm rainfall. With the current availability of large-storage, high-speed computers, the rainfall intensities can be analyzed and more realistic IDF relations developed. Also with the large computing capacities available today, the areal average maximum storm rainfalls that occur over various durations and specified areas can be calculated. If this is done for various storms occurring over a reasonably long period of record, frequency analyses can be undertaken on spatial average rainfalls for rain areas of various sizes. A similar suggestion was made by Allen and DeGaetano (2005). This analysis was undertaken with seven years of data up to and including Currently pertinent data for 2006 and 2007 are being analyzed. This should add at least thirty percent more storms to the database. When analyzed the new, larger database likely will either reinforce the Page 9 / 10

10 Ltd validity of the reported ARF equations or strengthen them. In the seven years analyzed, the largest maximum rainfall occurred in clusters in frontal storms. Therefore, it is suggested that some current hydrologic design procedures be reviewed to consider this hydrometeorologic regime. Weather radar stations are located at least 30 sites throughout Canada and at many more throughout the world. In many of these locations there are dense enough rain gauge networks to undertake accurate radar signal-rainfall calibrations. Since it has been shown that not only do the ARF equations vary with storm type, but also with geographic region (Allen and DeGaetano, 2005 and Omolayo, 1993), it is recommended that the hydrology community consider undertaking both the analyses reported upon in this paper but also some of the suggested ones in other locations. If this were undertaken more meaningful spatial statistics of storms in various regions could be obtained. REFERENCES Resources, Massachusetts Institute of Technology, ) National Weather Service, Rainfall Frequency Atlas of the United States for Durations from 30 minutes to 24 Hours, U.S. Weather Bureau Technical Paper No. 4, Washington, D.C., U. S. Department of Commerce, ) Omolayo, A.S. On the Transposition of Areal Reduction Factors for Rainfall Frequency Estimation, Journal of Hydrology, Vol. 145, ) Woolhiser, D. A., and H. C. Schwalen, Area- Depth-Frequency Relations for Thunderstorm Rainfall in Southern Arizona, Technical Paper 527. Tucson: Arizona Agricultural Experiment Station, The University of Arizona, ) World Meteorological Organization, Manual for Depth- Area-Duration Analysis of Storm Precipitation, Geneva, Switzerland, ) World Meteorological Organization, Manual for Determination of Probable Maximum Precipitation, Geneva, Switzerland, ) Ahnert, P.R., etal, Proposed on-site precipitation processing system for WSR- 88D, Preprints, 21 st conf. On Radar Meteorology, Edmonton, AB, Canada, American Meteorological Society, 1983, ) Allen R.J. and DeGaetano A.T, Areal reduction Factors for Two Eastern United States Regions with High Rain-Gauge Density, Journal of Hydrologic Engineering, ASCE, July/August, ) Eagleson, P.S., Dynamic Hydrology, New York, McGraw-Hill, ) KijeSipi Ltd, Spatial Distribution of Design Storm Rainfall, Report prepared for the City of Edmonton, Ottawa, Ontario, ) KijeSipi Ltd, Spatial Analysis of Rainfall Over & Near Edmonton, Ottawa, Ontario, ) LeClerc, G. and Schaake J. C., Derivation of Hydrologic Frequency Curves, Report No. 142, Cambridge, MA, R. M. Parsons Laboratory of Hydrodynamics and Water Page 10 / 10